信抽樣及抽樣定理

1、1、結(jié)合抽樣定理，利用 MATLAB 編程實(shí)現(xiàn)信號(hào)經(jīng)過沖激脈沖抽樣后得到的抽樣信號(hào)及其 頻譜，并利用構(gòu)建信號(hào)，并計(jì)算重建信號(hào)與原升余弦信號(hào)的誤差。解：wm=2;wc=1.2*wm;Ts=1;dt=0.1;t1=-10:dt:10;ft=sinc(t1/pi);N=5000;k=-N:N;W=2*pi*k/(2*N+1)*dt);n=-100:100;nTs=n*Ts;fst=sinc(nTs/pi);subplot(221);plot(t1,ft,:),hold on;stem(nTs,fst),grid on;axis(-10,10,-0.4,1.1);xlabel(Time(sec),yl

2、abel(fs(t);title(Sa(t) 抽樣后信號(hào) ),hold off,Fsw=Ts*fst*exp(-j*nTs*W);subplot(222);plot(W,abs(Fsw),grid on;axis(-20 20 0 4);xlabel(omega),ylabel(Fs(w);title(Sa(t) 抽樣信號(hào)頻譜 );t=-10:dt:10;f=fst*Ts*wc/pi*sinc(wc/pi)*(ones(length(nTs),1)*t-nTs*ones(1,length(t);subplot(223);plot(t,f),grid on;axis(-10 10 -0.4 1.

3、1);xlabel(t),ylabel(f(t);title( 重建新號(hào) );error=abs(f-ft);subplot(224);plot(t,error),grid onxlabel(t),ylabel(error(t);title( 誤差 );2、結(jié)合抽樣定理，利用 MATLAB 編程實(shí)現(xiàn)升余弦信號(hào) 經(jīng)過沖激脈沖抽樣后得到的抽樣信號(hào)及其頻譜，并利用構(gòu)建升余弦信號(hào)，并計(jì)算重建信號(hào) 與原升余弦信號(hào)的誤差。解：wm=2;wc=1.2*wm;Ts=1;dt=0.1;t1=-10:dt:10;ft=(1+cos(t1)/2).*(heaviside(t1+pi)-heaviside(t1-pi

4、);N=5000;k=-N:N;W=2*pi*k/(2*N+1)*dt);n=-100:100;nTs=n*Ts;fst=(1+cos(nTs)/2).*(heaviside(nTs+pi)-heaviside(nTs-pi);subplot(221);plot(t1,ft,:),hold on;stem(nTs,fst),grid on;axis(-10,10,-0.4,1.1);xlabel(Time(sec),ylabel(fs(t);title(Sa(t) 抽樣后信號(hào) ),hold off,Fsw=Ts*fst*exp(-j*nTs*W); subplot(222); plot(W,abs(Fsw),grid on; axis(-20 20 0 4); xlabel(omega),ylabel(Fs(w); title(Sa(t) 抽樣信號(hào)頻譜 );t=-10:dt:10;f=fst*Ts*wc/pi*sinc(wc/pi)*(ones(length(nTs),1)*t-nTs*ones(1,length(t); subplot(223);plot(t,f),grid on; axis(-10 10 -0.4 1.1); xlabel(t),ylabel(f(t); title( 重建新號(hào) ); error=abs(f-f